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Let f:{1 , 2,3 ,} rarr {a, b, c} be one-...

Let `f:{1 , 2,3 ,} rarr {a, b, c}` be one-one, and onto function given by `f(1)=a, f(2)=b` and `f(3)=c`. Shów that there exists a function `g:{a, b, c} rarr {1,2,3.}` such that `g o f=I_x` and `f o g=, I_ y` where, `X={1,2,3}` and `Y={a, b, c}`

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Show that if f: A rarr B and g: B rarr C are onto, then gof : A rarr C...

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  2. Are 'f' and 'g' both necessarily onto, if gof, is onto?

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  3. Let f:{1 , 2,3 ,} rarr {a, b, c} be one-one, and onto function given b...

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  4. Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. ...

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  5. Consider of f : N rarrN and h : N rarr R defined as f(x) = 2x, g(y) = ...

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  6. Let S = {1, 2, 3}. Determine whether the function f : S rarr S defined...

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  7. Let f : {1, 3, 4} rarr {1, 2, 5} and g : {1, 2, 5} rarr (1, 3} be gi...

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  8. Let f, g, and h be functions from R to R. Show that (f + g) o h = fo...

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  9. Find f o g and g o f f(x) = |x| and g(x) = |5x -2|

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  10. If f(x) =(4x + 3)/(6x - 4), x ne 2/3, show that (fof)(x) = x, for all ...

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  11. State with reason whether the following functions have inverse f : {...

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  12. Show that f:[-1,1]toR given by f(x)=frac(x)(x+2) is one-one.

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  13. Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. ...

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  14. Consider f:R^+to[-5, infty) given by f(x)=9x^2+6x-5. Show that f is ...

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  15. Let f : X rarr Y be invertible, show that f has unique inverse

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  16. Consider f : {1, 2, 3} rarr {a, b, c} given by f(1) = a, f(2) = b and ...

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  17. Let f : X rarr Y be invertible, show that the inverse of f^(-1) = f, ...

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  18. If f : R rarr R be given by f(x) = (3 - x^3)^(1/3), then (f o f) (x) i...

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  19. f : R - {(-4)/3} rarr R be a function defined as f(x) = (4x)/(3x +4). ...

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  20. Can you define a function from 'RxR rarr R' such as 'f3: RxR rarr, R' ...

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